A correspondence between higher Adams differentials and higher algebraic Novikov differentials at odd primes

Abstract

This paper studies the higher differentials of the classical Adams spectral sequence at odd primes. In particular, we follow the “cofiber of τ \tau philosophy” of Gheorghe, Isaksen, Wang, and Xu [Acta Math. 226 (2021), pp. 319–407; Publ. Math. Inst. Hautes Études Sci. 137 (2023), pp. 107–243] to show that higher Adams differentials agree with their corresponding higher algebraic Novikov differentials in a certain range.